Let's see competent ancient races.
The Xeelee and Photino Birds have been brought up, and those are the first that come to mind. Particularly the Xeelee given the sheer magnitude of their opponent, and their ultimate solution to avoid defeat and extermination.
In the Schlockverse both the Dark Matter entities and the Gate Keepers have had their asses kicked around by uppity humans and their allies, upsetting plans that they've had in motion for hundreds of thousands of years. Therefore they totally and absolutely don't count as competent.
If I could remember a bit more about Exalted I might be able to come up with a few. The problems with
that setting isn't that the ancients weren't competent, but rather that they were just a little
too competent at stabbing each other in the back.
In WH40k the C'tan and Necrons are highly competent, both from their behavior during the War in Heaven and in the current "present" of the setting. The Old Ones... not so much, seeing as their short-sightedness in dealing with the Immaterium lead to their own demise, and that of most sentient life in the local galactic cluster. There's also the issue that much of what's fucked up in the "present" of the setting is their fault, but that's really more an issue of the Old Ones being gigantic assholes.
The Eldar can be pretty competent as far as ancient races go, sometimes scarily so, but they are also responsible for a catastrophe similar to the one that wiped out the Old Ones, though smaller in scale. I can forgive them that since debauchery was pretty much written into their genetic code,
and they have learned from their mistakes of the past such that they are still major players in the galactic scale.
From the Star Control setting, there's the Ur-Quan, who successfully conquered the entire galaxy. They were only defeated by the younger races because they were a tad too busy having a religious civil war to pay attention to the player's shenanigans. This was entirely justifiable because if the
Sa-Matra was equivalent to
USS Montana (the planned BB-67) then the player's ship was equivalent to
USS Fletcher (WW2 era), and everyone else was stuck with the equivalent of mid-19th century ironclads.
From what little I know of it, the main plot of Lensmen revolves around one competent ancient race attempting to create a psychic WMD in order to destroy their equally ancient and scarily competent enemies. This in a universe where the major powers can play billiards with planetary bodies.
In Doctor Who, depending on the episode/writer, the Daleks can be both very ancient, and very competent. The Time Lords are always very ancient, but their competence is highly dependent on who's writing, and I am to understand they are inept more often than not.
The cute aliens that shit dark matter in Futurama have managed to save the universe a couple of times. Granted they needed Fry's help to do it, but they didn't have much choice in the matter.